Single Phase and Three Phase Wattmeters and Energy Meters

SINGLE PHASE AND THREE PHASE WATTMETERS AND ENERGY METERS

Single Phase Wattmeter

Single phase power is measured by wattmeter. It gives the direct indication of power. It also takes account on the power factor.

At transient condition importance are given to the instantaneous power. At steady state condition importance are given to the average value of power over a cycle. Single phase wattmeter indicates the average value of power.

Electrodynamometer wattmeter, ferrodynamic wattmeter and low power factor (LPF) wattmeter are used for the measurement of single phase AC power.

Electrodynamometer Wattmeter

It consist of two coils,

1. Fixed coil (or) field coil

2. Moving coil (or) voltage coil

Fixed coil is divided into two halves and it is connected in series with the load. It carries the current in the circuit so it is also called as current coil (C.C). It is made up of heavy wire. It is laminated to avoid eddy current loss. Maximum current is limited to 20 A.

For power measurement associated with large load current, 5A wattmeter with a current transformer is used.

Fixed coil is connected in series for a basic measurement range. To increase wattmeter current range to twice its original value, C.C can be connected in parallel. Shunts are not used for extension of current range because they canse temperature errors.

Moving coil is connected across the voltage. It carries a current proportional to the voltage, a high non inductive resistance is connected in series with this coil. This coil is called as pressure coil (P.C) and it is mounted on a pivoted spindle. Series resistance limits the current flow through this coil.

Both the coils are air cored. Voltage rating of wattmeter is usually limited to 600V. For higher voltage, pressure coil is designed for 110V and a potential transformer is used along with the wattmeter.

Control torque is produced by spring control system. Damping torque is provided by air friction damping. Eddy current and electromagnetic damping are not used because of weak operating force. Mirror type scale and knife edged pointer is used.

Principle:

Current through the current coil creates a flux around it. Current proportional to the voltage through the pressure coil creates its own flux around the coil. These two fluxes creates a force between them. This causes a deflecting torque.

Torque equation:

instantaneous torque of electrodynamometer instrument is

T_i = i_p i_c d M/d Q

where i_p and i_c are the instantaneous value of current in the P.C and C.C respectively.

Instantaneous value of voltage across the P.C is v_p = √2 V_p sinωt

P.C is considered as purely resistive because of its very high resistance. Current in P.C is in phase with voltage and its instantaneous value is,

i_p =√2I_p ………(1)

current in C.C lags the voltage in phase by an angle 'ϕ'

 instantaneous value of 'I' in C.C is,

i_c = √2 I_c sin(ωt - ϕ) ……….(2)

From (1) & (2),

T_i = √2 I_p sinot √2 I_c sin (ωt - ϕ).dM/dQ

we know that

sin A sin B = ½ [cos (A-B) - cos (A + B)]

here A = ωt and B = ωt - ϕ

T_i = √2 I_p √2 I_c ½ [cos (ωt - ωt + ϕ) - cos (ωt + ωt - ϕ)].dM/dƟ

T_i = I_p I_c [cosϕ - cos (2ωt - ϕ)].dM/dƟ

From the above equation it is clear that the component of power varies as twice the frequency of current and voltage.

Averge deflecting torque, T_d = 1/T ₀∫^T T_i d (ωt)

T_d = 1/2π ₀∫^{2 π} I_p I_c [cosϕ - cos (2ωt - ϕ)].dM/dƟ . dωt

T_d = I_p I_c cosϕ.dM/dƟ

T_c = kƟ by spring control.

At final steady state, T_c = T_d

kƟ = I_p I_c cos ϕ dM/dƟ

Ɵ = VI/R_p cos ϕ dM/dƟ . 1/k  

Ɵ = ﴾k₁ . dM/dƟ﴿. VI cos ϕ

deflection, Ɵ ∞ power

Scale is uniform over the range in which dM/dƟ is constant.

Advantages:

1. It indicates average value of power

2. Accurate reading

3. Damping is effective

4. No hysteresis error.

Disadvantage:

1.T_d is small

2. Error occurs due to the inductance of the P.C.

3. Not suited for low power factor circuits

Ferrodynamic Wattmeter

In this type of wattmeter, core is made up of iron. Low loss iron increases T by increasing flux density.

Fixed coil is wound on a laminated core. core is having pole pieces. Moving coil is placed over a hook shaped pole piece.

The iron losses make the flux de produced by the C.C to lag behind 'I' by an angle '∞'.

deflection, Ɵ = I_p I dM/dƟ cos (ϕ + ∞ - β)

Ɵ = C₁ dM/dƟ VI cos (ϕ + ∞ - β)

If ∞ = β, Ɵ = C₁ dM/dƟ VI cos ϕ

Ɵ = C₂ P

Where C₁ & C₂ are constants, thus the phase angle error will be zero. creep occurs in P.C because the P.C tries to take up a position where it links with maximum flux. Creep is a small but continuous change in position of the P.C on the hook when only the P.C is energised. (C.C is not energised). Creep is eliminated by using compensating coil.

In order to make a = β, 'β' angle should be increased, for this inductance of P.C should be increased. This high inductance is achieved by unifilar winding of series resistor. This high inductance and iron losses causes error, in reading. To eliminate this error a capacitor is used in parallel to the moving coil and a part of its series resistance.

 Advantage:

1. Less sensitive to external magnetic field

2. High T_d which is proportional to average power

3. Scale is upto 270.

Disadvantage:

1. Error due to non linearity of magnetization curve

2. Large eddy current and hysteresis losses in core cause errors.

Low Power Factor Wattmeter

Ordinary electrodynamometer wattmeter is not suited for the measurement of in low powerfactor circuits because 1. it has low T_d value and 2. inductance of P.C creates large errors at low power factors.

So some special changes or compensations are provided to ordinary electrodynamometer wattmeter to make it suitable for low power factor circuits. Such changes are listed below.

1. Pressure coil current (I_p):

P.C circuit is designed with low resistance, so this increases the current flows through the P.C and increases T_d.

I_p in LPF wattmeter ~ 10 (I_p in ordinary wattmeter)

2. Wattmeter connection:

Power loss in the coil connected to the load side is high. (either C.C or P.C). This is eliminated by providing compensating coil in series with the P.C. This compensating coil provides compensation for P.C current (Ip) in LPF circuit.

3. Inductance of pressure coil:

Inductance of P.C cause error in readings. This error is equal to VI sinϕ tan β The value of ϕ is large in case of LPF circuit and this automatically results in very high error.

This error is eliminated by a capacitor placed in parallel to a portion of series resistor connected with the P.C.

4. Small control torque:

LPF wattmeter is designed to have a small control torque. This small T_c helps for full scale deflection in LPF.

Thermocouple Wattmeter

In this circuit, two thermocouples are connected in such a way that they sense the heat generated by the two heter elements.

A galvanometer is connected between these two thermocouple

Emf across the galvanometer = e₁ - e₂

where e₁ is the emf generated by the first thermocouple. and e₂ is the emf generated by the second thermocouple.

R_H is the resistance of the heater element.

T_d ∞ vi (instantaneous power).

In this type two thermocouples are assumed to be identical. Thermal watt converter is used for measuring power in AC circuits.

Thermal watt converter consist of two heater element, two thermocouple, current and potential transformer arrangement. The plain arrowmark indicates the current flows from C.T and the flagged arrowmark indicates the current flows from P.T. In heater A, two currents flows in the same direction (S²). In heater B two currents flows in the opposite direction (D²). Thermocouple A & B senses the heat produced by the heater A & B respectively.

From the phasor diagram,

S² = V² + I² + 2VI cosϕ

D² =V² + I² - 2VI cosϕ

S² - D² = 4 VI cos ϕ

power = ¼ (S² - D₂)

where k is the constant.

voltage indicated by the millivoltmeter is E ∞ K (S² - D²)

E ∞ power

Hall Effect Wattmeter

When a current is allowed to pass through a conductor element, at the same time a magnetic field is applied perpendicular to the direction of current flow. A voltage is developed at the transverse side of the conductor. This effect is called hall effect, and the voltage developed is called hall voltage. This hall effect is used for the measurement of power.

Hall effect wattmeter is also called as hall effect multiplier. In this current is passed through the current coil and it produces a magnetic field perpendicular to the hall effect element. A current i proportional to the voltage is passed through the hall effect element. The current is limited by R. The output voltage is given by

V_H = K_H i_p B/t

Where K_H is the hall co-efficient, B is the flux density and t is the thickness of the hall element.

Here B ∞ i and

i_p ∞ v

V_H ∞ V.i

output voltage is proportional to the instantaneous power. The voltmeter connected at the output terminals is calibrated interms of power. The main advantage of this method is : its output can be used for further processing or for control applications.

Three Phase Wattmeter

A electrodynamometer type three phase wattmeter consists of two elements. A current coil along with its pressure coil is called as an element. Two moving coils (P.C's) are mounted on the same spindle.

The connections of this wattmeter is the same as that of two wattmeter method using two single phase wattmeters.

Here T_d of I^st element ∞ P₁

T_d of II^nd element ∞ P₂

Total deflecting torque o P₁ + P₂ ∞ power.

Error occurs if any mutual interference exist between the two elements. To eliminate this a laminated iron shield may be used or a compensation is provided by using weston's method.

Resistance may be adjusted to nullify the mutual interference effect.

Advantages:

1. Direct indication of three phase power.

2. High accuracy.